On Second-Order Variational Analysis of Variational Convexity of Prox-Regular Functions

Variational convexity, together with ist strong counterpart, of extended-real-valued functions has been recently introduced by Rockafellar. In this paper we present second-order characterizations of these properties, i.e., conditions using first-order generalized derivatives of the subgradient mappi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Set-valued and variational analysis Jg. 33; H. 1; S. 8
1. Verfasser: Gfrerer, Helmut
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Netherlands 01.03.2025
Springer Nature B.V
Schlagworte:
Analysis
Applied mathematics
Computational mathematics
Convexity
Localization
Mapping
Mathematical functions
Mathematics
Mathematics and Statistics
Neighborhoods
Optimization
Regularity
Research Article
Tilt-stable local minimizers
90C31
49J53
49J52
Coderivative
Variational strong convexity
Variational convexity
Subspace containing derivative
ISSN:1877-0533, 1877-0541
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Variational convexity, together with ist strong counterpart, of extended-real-valued functions has been recently introduced by Rockafellar. In this paper we present second-order characterizations of these properties, i.e., conditions using first-order generalized derivatives of the subgradient mapping. Up to now, such characterizations are only known under the assumptions of prox-regularity and subdifferential continuity and in this paper we discard the latter. To this aim we slightly modify the definitions of the generalized derivatives to be compatible with the f -attentive convergence appearing in the definition of subgradients. We formulate our results in terms of both coderivatives and subspace containing derivatives. We also give formulas for the exact bound of variational convexity and study relations between variational strong convexity, tilt-stable local minimizers and strong metric regularity of some truncation of the subgradient mapping.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-025-00744-8